_0^ /2 ^2 x ,dx = - Vidyadip

MCQ

$\int_0^{\pi /2} {{{\cos }^2}x\,dx = } $

A
$1 - \frac{\pi }{4}$
B
$1 + \frac{\pi }{4}$
✓
$\frac{\pi }{4}$
D
$\frac{\pi }{2}$

✓

Answer

Correct option: C.

$\frac{\pi }{4}$

c
(c) Using gamma function,

$\int_0^{\pi /2} {\,\,{{\cos }^2}x\,dx} $

$=\frac{{\Gamma \left( {\frac{3}{2}} \right)\Gamma \left( {\frac{1}{2}} \right)}}{{2\Gamma (2)}}$

$= \frac{{\frac{1}{2}\Gamma \left( {\frac{1}{2}} \right)\Gamma \left( {\frac{1}{2}} \right)}}{{2.1.\Gamma (1)}} = \frac{\pi }{4}$.

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